The story roves over triumphs — Meir’s raising of an astonishing $50 million from American Jews to boost Israel’s self-defense, her central role in its nationhood, her delirious reception in Moscow by long-oppressed Jews there — and such difficult moments as the postwar internment of Jewish refugees in camps on Cyprus, where many children died.

It also gets deeply personal, though typically with Meir’s trademark humor. Speaking of her extramarital affairs (she and Morris were long separated), she scolds the audience: “I never even told the children this. Why would I tell all of you?”

She also dishes that Dayan is “a very busy lover,” adding: “I always wondered, did he take the eye patch off?”

The balcony of the title actually is two: one at her flat in Tel Aviv, overlooking the sea; and one at a place called Dimona, whose significance is shrouded in mystery toward the end of the play.

The production’s one false note is the way the name Dimona is dropped, with a melodramatic touch that’s at odds with the play’s otherwise quietly arresting feel. (Though not so quiet when the bombs are dropping; the sound effects could stand to be dialed back a notch, too.)

Suffice to say that Dimona ties in with the story’s central question of whether Meir might resort to the nuclear option as Israel’s last desperate bid for survival against Arab attacks.

As much as the late Gibson (whose earlier, multicharacter play “Golda” was a Broadway flop) lets Meir make a case for the Zionist cause that built Israel, it doesn’t come off as stridently partisan. At one point, Meir speaks in sympathy for “our neighbors who want a state, too.”

But it makes clear that Meir, who resigned a year after the war and died four years later, hardly knew the word surrender.

“Survival is a synonym, maybe, for being Jewish,” as she says in the play.

A sentiment both sobering and hopeful, and one right in tune with this play’s bittersweet intimations.